A vertical wall stands away from a point on level ground

PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials

Problem

A vertical wall stands

40\,\text{m}

away from a point

O

on level ground. A ball is thrown from

O

with speed

30\,\text{m\,s}^{-1}

so that it hits the wall at a point

10\,\text{m}

above the ground. Neglect air resistance and take

g = 9.8\,\text{m\,s}^{-2}

. (i) Derive an expression for the time taken by the ball to reach the wall in terms of the angle of projection

\theta

. (ii) Using the conditions given, obtain the equation satisfied by

\theta

and hence calculate all possible angles of projection that allow the ball to strike the wall at the specified point. Give each value of

\theta

correct to one decimal place.